The Elastic Critical Load factor option uses a matrix analysis method to identify the lowest buckling mode of the structure. This method is based on the geometric stiffness matrix method, which modifies the standard stiffness matrix to account for the compressive force in an element. Where an element has a compressive force, the bending stiffness of the member is reduced, whereas a tensile force will increase the bending stiffness of a member. For a member loaded to its Euler Critical Buckling load, the Geometric stiffness method will reduce the bending stiffness of the member to zero.
The Elastic Critical Load factor is the elastic buckling load divided by the axial load on a member. For each individual load case, the axial load on the member is derived from the analysis of the particular load case.
With the Elastic Critical Load option active for a load case, the analysis of that load case will find the load factor at which the analysis no longer has a solution, indicating the structure is no longer stable. An iterative approach is used to find the load factor at which buckling occurs.
The results of the Elastic Critical Buckling analysis are given the Graphical Analysis Outputs, accessed by going to Results>Graphical Analysis Results. The Elastic Buckling factor is reported in the right-hand pane for those load cases where the Elastic Critical Load Factor option was activated.
In the Graphical Analysis Output, the Elastic Critical Buckling mode shape can also be shown graphically for any load case where the analysis option was active.
The Elastic Critical Buckling Load Factor method identifies the largest factor at which the analysis no longer completes, indicating the system of equations can no longer be solved. This indicates the structure is no longer stable. However, the instability may occur when a single member becomes unstable, or it may indicate the overall structural system has become unstable.
Elastic Critical Buckling Load Factor versus alpha-crit analysis
Both the Eurocode and British Standards provided a method to calculate the factor by which the design load would need to be increased to cause elastic instability in the global frame. In the Eurocode this is the alpha-crit factor, while in the British Standards this was the lambda-crit factor. Both the alpha-crit and lambda-crit calculations are based on the sway buckling mode of the structure, being based on the horizontal deflection under the horizontal design load. The aim of the alpha-crit and lambda-crit methods is to determine the global instability mode of the structure based in the initial elastic stiffness and the lateral deflections of the structure.
In a structure where the global instability is dominant and the whole structure buckles first, then the Elastic Critical Load factor method would be expected to give a similar Elastic Load factor as the alpha-crit and lambda crit-methods. However, if the buckling of an axially loaded member dominates the analysis and it is this Elastic Critical factor that the Elastic Critical method identifies, then the buckling mode identified will not be that of the global structure and therefore it is highly likely that the Elastic Critical Load factor method will result in a significantly different load factor than would result from the alpha- or lambda-crit methods.
The Graphical Analysis Output allows the display of the Elastic Critical Buckling Mode shape. The displays the deformed shape of the structure. To determine if the buckling shape is global, it is necessary to review the overall mode shape and make an engineering judgement.